Cell movement has essential functions in development, immunity, and cancer. Various cell migration patterns have been reported, but no general rule has emerged so far. Here, we show on the basis of experimental data in vitro and in vivo that cell persistence, which quantifies the straightness of trajectories, is robustly coupled to cell migration speed. We suggest that this universal coupling constitutes a generic law of cell migration, which originates in the advection of polarity cues by an actin cytoskeleton undergoing flows at the cellular scale. Our analysis relies on a theoretical model that we validate by measuring the persistence of cells upon modulation of actin flow speeds and upon optogenetic manipulation of the binding of an actin regulator to actin filaments. Beyond the quantitative prediction of the coupling, the model yields a generic phase diagram of cellular trajectories, which recapitulates the full range of observed migration patterns.

What is the fastest way of finding a randomly hidden target? This question of general relevance is of vital importance for foraging animals. Experimental observations reveal that the search behaviour of foragers is generally intermittent: active search phases randomly alternate with phases of fast ballistic motion. In this letter, we study the efficiency of this type of two states search strategies, by calculating analytically the mean first passage time at the target. We model the perception mecanism involved in the active search phase by a diffusive process. In this framework, we show that the search strategy is optimal when the average duration of "motion phases" varies like the power either 3/5 or 2/3 of the average duration of "search phases", depending on the regime. This scaling accounts for experimental data over a wide range of species, which suggests that the kinetics of search trajectories is a determining factor optimized by foragers and that the perception activity is adequately described by a diffusion process. PACS numbers:Searching for a randomly located object is one of the most frequent tasks of living organisms, be it for obtaining food, a sexual partner or a shelter [1]. In these examples, the search time is generally a limiting factor which has to be optimized for the survival of the species. The question of determining the efficiency of a search behaviour is thus a crucial problem of behavioral ecology, which has inspired numerous experimental [1,2,3,4,5] and theoretical [6,7,8,9,10] works . It is also relevant to broader domains such as stochastic processes theory [11,12], applied mathematics [13] and molecular biology [14,15].Anyone who has ever lost his keys knows that instinctively we adopt an intermittent behaviour combining local scanning phases and relocating phases. Indeed, numerous studies of foraging behaviour of a broad range of animal species show that such an intermittent behaviour is commonly observed and that the durations of search and displacement phases vary widely[1, 2, 3]. The spectrum, which goes from cruise strategy (ex. for large fishes that swim continuously such as tuna), to ambush or sitand-wait search, where the forager remains stationary for long periods (such as rattlesnake), has never been interpreted quantitatively. The intermittent strategy, often referred to as "saltatory" [2,3], can be understood intuitively when the targets are "difficult" to detect and sparsely distributed, as it is the case for many foragers (such as ground foraging birds, lizards, planktivorous fish...): since a fast movement is known to significantly degrade perception abilities [2,3], the forager must search slowly. Then, it has to relocate as fast as possible in order to explore a previously unscanned space, and search slowly again.Even though numerous models based on optimization of the net energy gain [4,5,6] predict an optimal strategy for foragers, the large number of unknown parameters used to model the complexity of the energetic constraint, renders a quantitative comparison wi...